Estimating the Number of Balloons Needed to Lift You Off the Ground

[ashvuck101]

Homework Statement

To an order of magnitude, how many helium-filled toy balloons would be required to lift you off the ground? Helium is an irreplaceable resource so develop a theoretical answer rather than an experimental one.

Homework Equations

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The Attempt at a Solution

ok i know that 1L of helium lifts 1 gram

given that the balloon i am using is 8.8181L in volume
V=4/3pi (12.5)^3

from that i divide 81.81/weight
weight=(60000)grams

=7333.86 balloons are need

i kno that but i want to calculate this using rho and density of air etc can anyone help??

 

[anathema]

Hello,

As a fellow scientist, I would like to offer my perspective on this question. First, I want to commend you for considering the importance of helium as a limited resource and seeking a theoretical answer rather than an experimental one. This shows your dedication to scientific principles and responsible resource management.

To answer your question, we must first understand the concept of buoyancy. According to Archimedes' principle, an object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. In this case, we can consider the air around us as the fluid and the helium-filled balloon as the object.

The buoyant force, Fb, can be calculated using the equation Fb = ρVg, where ρ is the density of the fluid (air in this case), V is the volume of the displaced fluid (equal to the volume of the balloon), and g is the acceleration due to gravity. In this case, we can assume g to be 9.8 m/s^2.

Now, to determine the number of balloons needed to lift you off the ground, we need to calculate your weight and compare it to the buoyant force of the balloons. Let's assume your weight to be 600 N (approximately 60 kg). Using the same volume of the balloon provided in the forum post, we can calculate the density of the helium needed to lift you off the ground.

ρ = W/Vg = 600 N / (8.8181 L * 9.8 m/s^2) = 6.89 kg/m^3

This is the density of the helium needed to lift you off the ground. Now, to determine the number of balloons, we can use the ideal gas law, PV = nRT, where P is the pressure (equal to atmospheric pressure), V is the volume of the balloon, n is the number of moles of helium, R is the gas constant, and T is the temperature (assumed to be room temperature).

Rearranging this equation to solve for n, we get n = PV/RT. Let's assume the pressure to be 1 atm, the volume of the balloon to be 8.8181 L, and the temperature to be 298 K (room temperature). Plugging in these values, we get n = (1 atm * 8.8181 L) / (0.082 L atm/mol K * 298 K) =